Related papers: An Adaptive Algorithm Employing Continuous Linear …
We study adaptive approximation algorithms for general multivariate linear problems where the sets of input functions are non-convex cones. While it is known that adaptive algorithms perform essentially no better than non-adaptive…
Most commonly used \emph{adaptive} algorithms for univariate real-valued function approximation and global minimization lack theoretical guarantees. Our new locally adaptive algorithms are guaranteed to provide answers that satisfy a…
Algorithms which compute locally optimal continuous designs often rely on a finite design space or on repeatedly solving a complex non-linear program. Both methods require extensive evaluations of the Jacobian Df of the underlying model.…
Automatic numerical algorithms attempt to provide approximate solutions that differ from exact solutions by no more than a user-specified error tolerance. The computational cost is often determined \emph{adaptively} by the algorithm based…
We present a fully iterative adaptive algorithm for the numerical minimization of strongly convex energy functionals in Hilbert spaces. The proposed approach, which we first present in abstract form, generates a hierarchical sequence of…
Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…
A key assumption in the theory of nonlinear adaptive control is that the uncertainty of the system can be expressed in the linear span of a set of known basis functions. While this assumption leads to efficient algorithms, it limits…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
A numerical method is developed to solve linear semi-infinite programming problem (LSIP) in which the iterates produced by the algorithm are feasible for the original problem. This is achieved by constructing a sequence of standard linear…
In this article a unified approach to iterative soft-thresholding algorithms for the solution of linear operator equations in infinite dimensional Hilbert spaces is presented. We formulate the algorithm in the framework of generalized…
We prove the quasi-optimal convergence of a standard adaptive finite element method (AFEM) for nonlinear elliptic second-order equations of monotone type. The adaptive algorithm is based on residual-type a posteriori error estimators and…
In our recent publication [1] we presented an exponential series approximation suitable for highly accurate computation of the complex error function in a rapid algorithm. In this Short Communication we describe how a simplified…
We propose a new method to design adaptation algorithms that guarantee a certain prescribed level of performance and are applicable to systems with nonconvex parameterization. The main idea behind the method is, given the desired…
We propose an adaptive iteratively linearized finite element method (AILFEM) in the context of strongly monotone nonlinear operators in Hilbert spaces. The approach combines adaptive mesh-refinement with an energy-contractive linearization…
In this paper, we discuss adaptive approximations of an elliptic eigenvalue optimization problem in a phase-field setting by a conforming finite element method. An adaptive algorithm is proposed and implemented in several two dimensional…
We consider the problem of approximating a given element $f$ from a Hilbert space $\mathcal{H}$ by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the…
We consider linear problems in the worst case setting. That is, given a linear operator and a pool of admissible linear measurements, we want to approximate the values of the operator uniformly on a convex and balanced set by means of…
We consider an incremental approximation method for solving variational problems in infinite-dimensional Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite collection of subproblems is…
The classical alternating minimization (or projection) algorithm has been successful in the context of solving optimization problems over two variables. The iterative nature and simplicity of the algorithm has led to its application to many…
In recent years, functional linear models have attracted growing attention in statistics and machine learning, with the aim of recovering the slope function or its functional predictor. This paper considers online regularized learning…